Recent observations have conclusively proven that the millisecond oscillations observed during thermonuclear X-ray bursts from some accreting neutron stars are tracers of the stellar spin. The spin frequency distribution of the 13 known nuclear-powered pulsars cuts off well below the centrifugal breakup frequency for most neutron star models. This supports theoretical predictions that gravitational radiation losses can limit accretion torques in spinning up millisecond pulsars.